Spectral analysis finds wide application in identifying and quantitating analytes in a sample. One particular form of spectral analysis measures the amount of electromagnetic radiation which is absorbed by a sample. For example, an infrared spectrophotometer directs a beam of infrared radiation at or through a sample and measures the amount of infrared radiation absorbed by the sample throughout some range of radiation wavelengths. An absorbance spectrum may then be plotted which relates sample absorbance to radiation wavelength. The overall shape of the absorbance spectrum, including the wavelengths and relative magnitudes of peak absorbance values, is characteristic of the particular analytes in the sample and thus may be used to attempt to identify, generally or particularly, the analytes.
Moreover, the absorbance spectrum may also be used in an attempt to quantitate the concentrations of each analyte in the sample. In accordance with a well known relationship expressed by Beer's Law, the absorbance of an analyte in a sample is essentially proportional to the concentration of the analyte in the sample. Where an absorbance spectrum represents the absorbance of a single analyte in a sample, the concentration of the analyte may be easily determined by comparing the sample absorbance at at least one wavelength to the absorbance of a sample at the same wavelength containing a known concentration of the analyte.
The most usual analytical application, however, involves the spectral analysis of a sample containing a plurality of analytes, that is, a multicomponent sample. In multicomponent analysis, Beer's Law still applies and the observed absorbance spectrum for the multicomponent sample is considered to be substantially equal to the sum of the individual absorbance spectra for each of the analytes or components in the sample.
Methods and apparatus for the quantitation of analyte concentrations in multicomponent samples are known in the art. The prior methods and apparatus each require that absorbance spectra for a plurality of calibration samples be obtained. The calibration samples each include various predetermined concentrations of analytes which are thought to be the same analytes present in unknown concentrations in an unknown sample. A plurality of absorbance values at predetermined identical wavelengths are determined on each of the calibration spectra providing a set of absorbance values for each spectra. The sets are arranged as, for example, columns in an absorbance matrix, A. The known concentrations of the analytes also form a set of values for each calibration sample. All of the sets of concentration values for the calibration samples are arranged as columns in a concentration matrix, C. Using matrix mathematics, the absorbance matrix A is related to the concentration matrix C by a constant matrix K in accordance with the following expression: EQU A=K*C Equation 1
where "*" represents matrix multiplication. Using matrix mathematics, the constant matrix K is determined and the inverse thereof, P, is also determined, that is, P*A=P*K*C, or C=P*A
An absorbance spectrum is also determined for an unknown sample. Absorbance values are selected from the unknown sample spectrum at the same wavelengths used to determine absorbance values from the calibration spectra. The unknown sample absorbance values are arranged into a sample matrix S, a vector, and the concentrations of the analytes in the unknown sample may then be determined using the following relationship: EQU P*S=U, Equation 2
where the vector U should substantially equal the concentrations of the analytes in the unknown sample. As will be apparent to those skilled in the art, a matrix having either one row or one column may be called a "vector", and both "matrix" and "vector" may be used herein for such a matrix.
The method just described has several inherent disadvantages which limit the accuracy of the method and similar methods. The number of absorbance values selected from the calibration spectra and the wavelengths at which the absorbance values are determined influence the accuracy of the method. For example, absorbance values for wavelengths at which the calibration spectra exhibit absorbance peaks may be selected. However, the resulting representation of the calibration spectra is extremely limited and does not provide a detailed representation of such spectra.
In an effort to better represent the absorbance spectra, the number of absorbance values may be increased. However, increased numbers of absorbance values also increases the complexity and the time required to determine the P matrix and to determine the unknown sample concentration vector U. Even with a large number of absorbance values from each absorbance spectrum, the resulting sets of absorbance values still provide only a limited representation of the absorbance spectra.
Another drawback of the method described above is that the measured absorbance spectra may include some high-frequency noise introduced by the measurement method. The absorbance values selected from the spectra, however, will include the high frequency noise, further contributing to inaccurate unknown sample concentration results.
A further difficulty in the method is that it is first necessary to determine a base line for each spectrum to account for background absorbance. The determination of a base line can be somewhat arbitrary and, if improperly or inaccurately accomplished, further diminishes the accuracy of prior art quantitation methods.
The prior art method described above, as well as similar prior methods, include a further disadvantage in that the determination of the unknown sample concentration vector U assumes that the unknown sample includes only the analytes present in the calibration samples. The prior methods include no means for indicating that other analytes may be present in the sample and merely determine analyte concentrations as though only the analytes present in the calibration samples are present in the unknown sample. Consequently, the unknown sample analyte concentrations determined by prior methods and apparatus may be inaccurate and improperly indicate analyte concentrations which actually are not present.
Thus, there is a need for a multicomponent quantitative analytical method and apparatus which overcomes the limitations and disadvantages of prior art methods and apparatus. In particular, there is a need for a method and apparatus which more accurately represents the calibration sample spectra and unknown sample spectrum. There is also a need for a method and apparatus which is less influenced by measurement noise and which obviates the selection of base line to account for background absorbance. There is also a need for a method and apparatus which will indicate that the unknown sample includes analytes other than those present in the calibration samples.